Question : S, T, and U can complete a work in 40, 48, and 60 days, respectively. They received Rs. 10,800 to complete the work. They began the work together, but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has completed the remaining work alone. What is the share of S (in Rs.) from the total money?
Option 1: 4000
Option 2: 4320
Option 3: 4500
Option 4: 4860
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Correct Answer: 4860
Solution : S’s 1 day work =$\frac{1}{40}$ T’s 1 day work = $\frac{1}{48}$ U’s 1 day work = $\frac{1}{60}$ Let the work be completed in $x$ days, such that S worked for all $x$ days, T worked for $(x - 2)$ days, and U for $(x - 5)$ days. ⇒ $\frac{x}{40}+ \frac{x-2}{48} + \frac{x-5}{60}= 1$ ⇒ $6x + 5(x - 2) + 4(x - 5) = 240$ ⇒ $6x + 5x - 10 + 4x - 20 = 240$ ⇒ $15x = 270$ ⇒ $x = \frac{270}{15}=18$ days Hence, ratio of their share =$\frac{18}{40} ∶ \frac{16}{48} ∶ \frac{13}{60} = 27∶20∶13$ Sum of ratios = 27 + 20 + 13 = 60 $\therefore$ S’s share = $\frac{27}{60}× 10800 = 4860$ Hence, the correct answer is 4860.
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Question : Anshu, Swati, and Rajni can finish a work in 4 days if they work together. However, Anshu alone will take 9 days to complete the work, and Swati alone will complete the work in 12 days. How many days will Rajni alone take to complete the work?
Option 1: 18
Option 2: 12
Option 3: 24
Option 4: 16
Question : A and B together can finish a work in 30 days. They worked on it for 20 days and then B left. The remaining work was done by A alone in 20 days. In how many days can A alone finish the work?
Option 1: 48 days
Option 2: 50 days
Option 3: 54 days
Option 4: 60 days
Question : A, B and C can work separately in 18, 36 and 54 days. They started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work. In how many days was the work finished?
Option 1: 15 days
Option 2: 13 days
Option 3: 14 days
Option 4: 12 days
Question : A can finish a work in 20 days and B can complete the same work in 15 days. B worked for 9 days and left the job. In how many days can A alone finish the remaining work?
Option 1: 10 days
Option 2: 8 days
Option 3: 9 days
Option 4: 7 days
Question : Sara can finish a work in 18 days and Tara can complete the same work in 15 days. Tara worked for 10 days and left the job. In how many days can Sara finish the remaining work alone?
Option 1: 6
Option 2: 7
Option 3: 8
Option 4: 5
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